LCM from Prime Decomposition/Examples/132 and 154

Example of Use of LCM from Prime Decomposition

The lowest common multiple of $132$ and $154$ is:

$\lcm \set {132, 154} = 924$

Proof

\(\ds 132\)

\(=\)

\(\ds 2^2 \times 3 \times 11\)

\(\ds 154\)

\(=\)

\(\ds 2 \times 7 \times 11\)

\(\ds \leadsto \ \ \)

\(\ds 132\)

\(=\)

\(\ds 2^2 \times 3^1 \times 7^0 \times 11^1\)

\(\ds 154\)

\(=\)

\(\ds 2^1 \times 3^0 \times 7^1 \times 11^1\)

\(\ds \leadsto \ \ \)

\(\ds \lcm \set {132, 154}\)

\(=\)

\(\ds 2^2 \times 3^1 \times 7^1 \times 11^1\)

\(\ds \)

\(=\)

\(\ds 924\)

$\blacksquare$

Sources

• 1971: George E. Andrews: Number Theory ... (previous) ... (next): $\text {2-4}$ The Fundamental Theorem of Arithmetic: Exercise $9 \ \text {(b)}$